The Oil Drum

I've given this some thought myself, and concluded that it is possible to make C3S clinker, but not by the same route used in conventional kilns. Remember that 75% of PC kiln feed is limestone, and the limestone produces CO2 as it is calcined, so that about 80% of the CO2 produced in cement-making comes from the limestone, not the fuel. (and cement accounts for 5-7% of man-made CO2 globally!)

An alternative process uses molten calcium chloride, and has been around for decades.
CaCl2.H2O -> CaO + 2HCl
3CaO + SiO2 -> Ca3SiO5 (at about 700C)

Hydrated calcium chloride melts at about 180C, so the whole process can take place in liquid phase, with the silica in slurry form.

If there is an ocean or brine reservoir nearby, the CaCl2 can be made from limestone and MgCl2 brine by exchange
CaCO3 + MgCl2 -> MgCO3 + CaCl2

You also need a market for the hydrochloric acid.

The challenge here is firstly materials, because molten chlorides + HCl at high temp are extremely corrosive (remember there is water present). The whole reactor loop, and especially the solar absorber will have to be ceramic (carbides?) and able to withstand day/night thermal cycling. If you can figure this out you will be a hero.

Second challenge is business. The cement companies are global semi-monopolies with billions invested in conventional kilns, and won't change until they absolutely have to. They will buy carbon credits for decades first.